document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964177>Question 964177</A>: <I><SPAN STYLE=\"word-break: break-all;\"> martin wants to ship a souvenir baseball bat that is 16 inches long in this box. um i don't have the pic of the box but i will describe it to you. its 12 inches at the base. 9 inches on the other base and 8 inches on the height if that makes sense. the question asks: will martin be able to ship the bat in the box? show your work and explain your answer please... i am just so confused. the second question asks: martin finds another box he could use to ship the same bat in. the box is a cube, and has the least whole number edge lengths that will allow the bat to fit. what is the edge length of that box? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589147 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=589147\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is the base of the box:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28350%2C275%2C-1%2C13%2C-1%2C10%2Crectangle%280%2C0%2C12%2C9%29%2C%0D%0Agreen%28line%280%2C0%2C12%2C9%29%29%2Clocate%286%2C4.5%2Cgreen%28d%29%29%2C%0D%0Alocate%285.5%2C0%2C12%29%2Clocate%2812.1%2C5%2C9%29%2C%0D%0Alocate%28-.25%2C0%2CA%29%2Clocate%2812%2C0%2CB%29%2Clocate%2812%2C9.5%2CC%29%2C%0D%0Arectangle%2811.5%2C0.5%2C12%2C0%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The length of the diagonal AC (in inches) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28d%29=sqrt%2812%5E2%2B9%5E2%29=sqrt%28144%2B81%29=sqrt%28225%29=15 ALIGN=MIDDLE  ALT=\"green%28d%29=sqrt%2812%5E2%2B9%5E2%29=sqrt%28144%2B81%29=sqrt%28225%29=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > (so says Pythagoras).<BR>\n" );
document.write( "It is clear that you cannot lay down the bat on tha base of the box,<BR>\n" );
document.write( "along that diagonal, but there may be a way.<BR>\n" );
document.write( "However, you could rest one end of the bat on one corner of the base of the box,<BR>\n" );
document.write( "and see if the other end can fit above the opposite corner of the base,<BR>\n" );
document.write( "but still within the box.<BR>\n" );
document.write( "Let's see what that box would look in almost 3-D:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C320%2C-1%2C19%2C-1%2C15%2C%0D%0Aline%280%2C0%2C12%2C0%29%2Cline%280%2C0%2C0%2C8%29%2C%0D%0Aline%280%2C8%2C12%2C8%29%2Cline%2812%2C8%2C12%2C0%29%2C%0D%0Aline%286%2C14%2C18%2C14%29%2Cline%2818%2C14%2C18%2C6%29%2C%0D%0Aline%2812%2C0%2C18%2C6%29%2Cline%2812%2C8%2C18%2C14%29%2Cline%280%2C8%2C6%2C14%29%2C%0D%0Alocate%28-.25%2C0%2CA%29%2Clocate%2812%2C0%2CB%29%2Clocate%2818%2C6%2CC%29%2C%0D%0Alocate%2818.1%2C14.5%2CD%29%2Clocate%28-0.35%2C8.5%2CE%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > It does not look realistic, because I did not draw true perspective.<BR>\n" );
document.write( "For true perspective I should draw shorter the lines are supposed to be further back,<BR>\n" );
document.write( "for example making CD shorter than AE.<BR>\n" );
document.write( "Instead, I made them the same length.<BR>\n" );
document.write( "Maybe you could rest one end of the bat on one corner of the base of the box (A),<BR>\n" );
document.write( "and see if the other end can fit above the opposite corner of the base (C),<BR>\n" );
document.write( "but still within the box (maybe at D, or a little below D along line CD).<BR>\n" );
document.write( "We just need to measure the distance AD to see if the bat will fit.<BR>\n" );
document.write( "Let me draw the other edges and diagonals, as if the box were see-through<BR>\n" );
document.write( "(I will just make them different colors, instead of black):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C320%2C-1%2C19%2C-1%2C15%2C%0D%0Aline%280%2C0%2C12%2C0%29%2Cline%280%2C0%2C0%2C8%29%2C%0D%0Aline%280%2C8%2C12%2C8%29%2Cline%2812%2C8%2C12%2C0%29%2C%0D%0Aline%286%2C14%2C18%2C14%29%2Cline%2818%2C14%2C18%2C6%29%2C%0D%0Aline%2812%2C0%2C18%2C6%29%2Cline%2812%2C8%2C18%2C14%29%2Cline%280%2C8%2C6%2C14%29%2C%0D%0Alocate%28-.25%2C0%2CA%29%2Clocate%2812%2C0%2CB%29%2Clocate%2818%2C6%2CC%29%2C%0D%0Alocate%2818.1%2C14.5%2CD%29%2Clocate%28-0.35%2C8.5%2CE%29%2C%0D%0Alocate%285.5%2C0%2C12%29%2Clocate%2815%2C3%2C9%29%2C%0D%0Alocate%2818.1%2C10.5%2C8%29%2Clocate%289%2C3%2Cgreen%2815%29%29%2C%0D%0Ablue%28line%280%2C0%2C6%2C6%29%29%2Cblue%28line%2818%2C6%2C6%2C6%29%29%2C%0D%0Ablue%28line%286%2C14%2C6%2C6%29%29%2Cgreen%28line%280%2C0%2C18%2C6%29%29%2C%0D%0Ared%28line%280%2C0%2C18%2C14%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Since AC is horizontal and CD is vertical, angle ACD is a right angle, and triangle ACD is a right triangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28425%2C250%2C-1%2C16%2C-1%2C9%2C%0D%0Arectangle%2815%2C0%2C14.5%2C0.5%29%2Cline%2815%2C0%2C15%2C8%29%2C%0D%0Agreen%28line%280%2C0%2C15%2C0%29%29%2Cred%28line%280%2C0%2C15%2C8%29%29%2C%0D%0Alocate%28-.25%2C0%2CA%29%2Clocate%2815%2C0%2CC%29%2Clocate%2815.1%2C8.5%2CD%29%2C%0D%0Alocate%287%2C0%2Cgreen%2815%29%29%2Clocate%2815.1%2C4.5%2C8%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, according to the Pythagorean theorem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD=sqrt%2815%5E2%2B8%5E2%29=sqrt%28225%2B64%29=sqrt%28289%29=17 ALIGN=MIDDLE  ALT=\"AD=sqrt%2815%5E2%2B8%5E2%29=sqrt%28225%2B64%29=sqrt%28289%29=17\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So the box is big enough, and the bat fits.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Now, what about a square box, with side length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches?<BR>\n" );
document.write( "The length (in inches) of a diagonal of the base (like AC) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%2Bx%5E2%29=sqrt%282x%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2Bx%5E2%29=sqrt%282x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That diagonal and a vertical edge of length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches form a right angle,<BR>\n" );
document.write( "and with a line connecting opposite corners of the box (like AD) they form a right triangle.<BR>\n" );
document.write( "The distance between opposite corners of the box is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28sqrt%282x%5E2%29%29%5E2%2Bx%5E2%29=sqrt%282x%5E2%2Bx%5E2%29=sqrt%283x%5E2%29=sqrt%283%29x ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29=about+1.73 ALIGN=MIDDLE  ALT=\"sqrt%283%29=about+1.73\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9sqrt%283%29=about15.6 ALIGN=MIDDLE  ALT=\"9sqrt%283%29=about15.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so a cube-shaped box of edge length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches is too small,<BR>\n" );
document.write( "but for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10sqrt%283%29=about17.3 ALIGN=MIDDLE  ALT=\"10sqrt%283%29=about17.3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so a cube-shaped box of edge length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2810%29 ALIGN=MIDDLE  ALT=\"highlight%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches is large enough to fit the bat. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );